Why do only egg yolks and not whole eggs get used in a coconut - pecan frosting?

Can someon explain why we waste 4 egg whites in a coconut - pecan frosting for a German Sweet Chocolate cake instead of using 2 whole eggs?
Does the egg yolks give a flavor, consistency, color that whole eggs would detract from? I hate to experiment because the loss could be expensive.

It would change the flavor and consistency, yes. And color too for that matter, although that is not as big a deal.
You can store and even freeze the egg whites if you wish to avoid wasting them. But being the season for egg nog, you can also use them in there. If the recipe calls for 4 egg yolks mixed up and 4 egg whites whipped, just use 6 egg whites whipped up to thin it out some without detracting from the taste.

When I make Challah bread I end up with two egg whites. I thin them with 1-2 T of water and brush them on the bread to give some color and to hold the sesame and poppy seeds. I then keep them covered in the fridge and use them for the same thing on my Italian bread. I've kept them for over a week in a bowl sealed with plastic wrap with no ill effects. I bake bread so frequently that they never go to waste.

My Creme brulee's and hollandaise sauce, among other things call for just the yolks. Then I have cake recipes that call for extra (or only) egg whites. So, I just through the whites into containers, mark on top the date and how many and then pull them out when I need them. If I am using the whites and have a couple of yolks I will make hollandaise or a custard for dessert. I rarely waste either part of the egg!